On the sound field of an oscillating disk in a finite open and closed circular baffle

Tim Mellow, Leo Kärkkäinen

Abstract: Equations describing the radiation characteristics of a rigid disk in a finite open baffle are derived using a method similar to that used by Streng for a circular membrane based upon the dipole part of the Kirchhoff–Helmholtz boundary integral formula. In this case, however, a power series solution to the radiation integral is derived in order to eliminate the need for numerical integration. Hence, a set of simultaneous equations is obtained by simply equating the coefficients of the power series, which leads to two mathematical functions, one real and one imaginary, that can be applied to any radial velocity distribution. This provides an alternative method to obtain the sound scattered by a disk or the complementary hole in an infinite resilient screen according to Babinet’s principle. Using the principle of superposition (or Gutin concept), it is shown how the sound radiation characteristics of a disk radiating from just one side can be obtained by combining the radiation field of a disk in a finite baffle with that of a disk in an infinite baffle. This one-sided radiator may be interpreted as a disk in a thin, circular enclosure.